From what I've seen from the Japanese Wikipedia, names of communist figures (Mao Zedong, Deng Xiaoping, Xi Jinping) seem to be read with on'yomi (Mou Takutou, Tou Shouhei, Shuu Kinpei). On the other hand, names of some actors (Fan Bingbing, Jimmy Lin, Ruby Lin) seem to follow English practice (Fan Binbin, Jimii Rin, Rubii Rin), even though their articles are still titled using kanji. Other more internationally mainstream actors (Jackie Chan, Sammo Hung) get their names entirely transcribed from English (Jakkii Chen, Samo Han).

What are the common practices of reading names of modern Chinese people? Also, do newspapers use furigana for these names?

1 Answer
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Like with Korean names, which you asked in another question, the way Chinese names are written can also depend on contexts and the name being written.

As you pointed out, names of actors and people from British Hong Kong are often written in katakana and pronounced in Chinese or English manner, while those of political figures are usually written in kanji and read in Japanese on-yomi.

Unlike Korean names though, this is the case both in public and formal context (like broadcasting and newspaper) and in private and informal context (like chatting between friends) because it's more straightforward: people hear on-yomi, not Chinese, and they can write what they hear.